Η αλφαβήτα - Εικονογραφημένες καρτέλες και πρότυπες λέξεις - Τάξη Α
Ολότητα & η Ελλοχεύουσα Τάξη
230
ΟΛΟΤΗΤΑ ΚΑΙ Η ΕΛΛΟΧΕΟΥΣΑ ΤΑΞΗ
description
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Transcript of Ολότητα & η Ελλοχεύουσα Τάξη
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...................................................................................................................................................................6
.....................................................................................................................................................................8
1. ........................................................................................................16
:
.................................................................................................................................37
2. - ...................................................45
2.1 ........................................................................................................................................................45
2.2 .............................................................................................................46
2.3 ............................................................................................................51
2.4 ....................................................................61
2.5 .............66
3. ............................................68
3.1 .................................................................................................................................................68
3.2 ....................................................................................................................70
3.3 ........................................................................................................73
3.4 .........................................................................................................................77
3.5 , .............................................................84
4. ................................................................................87
4.1 .........................................................................87
4.2 ................................88
4.3 ...........................................................89
4.4
.........................................................................................................................91
4.4.1 Heisenberg............................................................................................91
4.4.2 Von Neumann .....................................................92
4.4.3 Einstein, Rosen Podolsky.......................................................................................93
4.5 BOHR EINSTEIN, ROSEN PODOLSKY-
................................................................95
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4.6
..................................................................................................................................................................................99
4.7
....................................................................................................................103
4.8 ....................................108
4.9 ...........................................................................110
4.10 HEISENBERG.........................................................................112
4.11 ..........................................................116
4.12 ........................................................................................121
4.13 -
........................................................................................................................................130
4.14 ............................................................................................................................................135
5. ( ).......................136
5.1 ...............................................................................................................................................137
5.2 ........................................................................................................................................................141
5.3 .....................................................................................................................................................144
5.4 ...................................................146
5.5 , ..................................................................147
5.6 ........................................................................................................149
5.7 ..............................................................................................................................155
5.7.1 ................................................................................155
5.7.2 - .................................................................156
5.7.3 .......................................................................156
5.7.4 - ( Einstein, Podolsky Rosen)....................................157
6. ( ).......................168
6.1 ...............................................................................................................................................168
6.2 - ............................................................171
6.3 ...............................................................................175
6.4 .......................................................................................178
6.5 ...................................................................................................................184
7. ...........................................................................187
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7.1 ...............................................................................................................................................187
7.2
187
7.3 ..........................................................194
7.4 ....202
7.5 .....................................................................................205
7.6 , ............209
7.7 .........................................................................................212
7.8 , , ........................................................................223
.............................................................................................................................................................231
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).
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. Heisenberg
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4.4.2 Von Neumann , , von
Neumann, .
(4), (5) (6) 1,
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4.4.3 Einstein, Rosen Podolsky
EPR ( Einstein, Rosen Podolsky).
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Heisenberg
. Einstein,
Rosen Podolsky ,
Heisenberg.
.
spin (), spin
-
/2 -/2 .
spin . spin
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.
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4.5 BOHR EINSTEIN, ROSEN PODOLSKY-
EPR Niels Bohr
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.
2. , ,
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3.
=S/m (1) m , S ,
= ReiS/, R S
.
4. V(x)
,
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.) -
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.
-
k,
, k.
, k/t (
, , .).
.
( Brown ).
,
. , , k,
, t (
).
= a(k/t) (6)
a . ,
,
, t,
= bt or |k| =b1/2(t)1/2 (7)
b ,
.
,
,
, .
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. (6),
k
k = a|k|/t = ab1/2/(t)1/2 (8)
(8) (7),
-
k k = ab (9)
k k
, ab, t.
Heisenberg, pq . , ab, . (9) Planck, h, Heisenberg.
x ab.
a
. b, ,
. b
, , , .
,
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) ,
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,
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,
.)
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b
t0, b .
- Planck, h,
( ).
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(t)2 (
). ,
= T = /b2 (10)
Boltzmann .
, , t, . (8)
, 2 .
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T = /b2 2b/t02 or t02 = a2/bT (11)
( )
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.
Heisenberg
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) .
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k = S/qk(q1,q2,,qk J1, J2,, Jn)
Qn = S/Jn(q1,q2,,qk J1, J2,, Jn) (12)
S , pk qk
, Jn Qn . ,
Jn . ,
,
, Hamiltonian
Jn Qn. Qn
.
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,
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,
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h Planck.
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(4) (12)
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. S , (4),
S, . S
= ReiS/. ,
, S = Im (In),
.
S .
(4)
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C, ,
qk ( ), . . (13) ,
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.
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, qk. ,
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n .
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.
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( R2) . R2
.
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,
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Bohr-Sommerfeld
,
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Sc
. (16),
.
-
1.
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, Qn.
2. Jn h.
, .
3. , Qn (
) . ,
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.
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( 2,
).
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, p(q1,q2,,qk), 1 (
, pk, qk . (12)).
5. = ReiS/, p(q1,q2,,qk) =
R2(q1,q2,,qk) S
.
5,
.
6.
, In, , ,
. , ,
, C, Ic = kcpkqk = Sc , S (
) C.
h
.
-
4.12 ,
.
,
,
.
, S, = ReiS/
, ,
( . (15))
S
h S ,
eiS/ .
S
,
de Broglie.
,
,
.
, (.., ).
,
.
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). , ,
.
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,
, .
-
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, v(x,t).
: (1)
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, (2), , ,
.
, (
).
= 0 (17)
, x
.
, (
).
. , , ,
, .
Lorentz, ..,
. (x,t)
(x, t). t. Lorentz,
= 0 = 0[t-vx/c2]/1-v2/c2 (18)
, c
2n, n . ,
x t.
= 0(t-vx/c2)/1-v2/c2 = 2n (19)
-
, m0,
= m0c2/1-v2/c2, p = m0v/1-v2/c2,
(Et - px) = 2n m0/0c2 (20)
m0c2/0 = ( )
,
, p , x (.., t = 0
. (20) . (16)).
, , ,
, ,
.
, .
, ,
. ,
m0c2/0 . (20)
h.
,
, .
, h, ,
,
,
.
,
.
,
, xli, , pli. i-
l- xli, pli
.
-
.
,
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,
.
. ,
, xli pli,
, , ,
.
. , S,
, xli, .
,
Pli = S/xli (xli,..., xlk) (21)
l .
,
Ic = k,lplkxlk = Sc (22)
.
pixi, ,
px = 2n . ,
.
,
.
-
Sc= 2n,
, ,
. ,
.
, m0c2/0 .
. ,
,
( ).
Ic = ck,l plkqlk
,
, .
, ,
Ic h,
Ic .
.
,
, h. ,
.
,
(., ).
, , . ,
, =j0/2, J = Sh,
S , E0 = S0.
-
E0 , E0 = m0c2.
m0c2/ 0 = S (23)
. (20)
(Et - px) = 2 m0c2/0 n = nSh = nh (24)
, , S ,
. ,
, m0c2/0 , .
,
, , Heisenberg. ,
, h,
- .
,
(
).
h.
,
.
. (
).
.
,
. ,
,
-
.
n- Jn n .
, Jn ,
n n = nt + 0n, n
n- . Jn n
, (12).
Bohr-Sommerfeld (16) , Jn = Sh,
S . ,
pn = 2 Jncosn, qn = 2 Jnsinn.
,
Qli li. ,
.
. ,
.
, Qli li, , ,
, , ,
.
,
Qli = ninpn = 2ninJncosnli = ninqn = 2ninJnsinn (25)
in in , n
.
Qli li
, Poisson ,
n(li/Jn Qli/n - li/n Qli/Jn) = 1
-
. (25),
nn = 1. (26)
. (25) Qli li,
n
( ). ,
(- ) ,
Lissajou
, .
, ,
, 2/n, , Qli li
, , ,
. Qli
li, , .
Qli = li = 0 , ,
(Qli)2 = 4mnmnJmJncosmcosn = 2mm2Jm (27)
(li)2 = 4mnmnJmJnsinmsinn = 2nn2Jn (28)
cosmcosn = sinmsinn = 0 m n (
cos sin
).
( J = h) .
. ,
(Qli)2 and (li)2.
Jn = h . (28)
(Qli)2 = 2mm2h (li)2 = 2nn2h
Schwarz
-
mn = m2 n2 m mm 2 (29)
. (26), (27) (28),
(Qli)2 (li)2 4h2 (30)
, , Heisenberg. Qli li - l-
,
2/n. , Heisenberg
.
. (30) 10
-
Brown.
Jn
, h, ,
Brown.
o
Heisenberg.
, ,
, ,
.
,
, 0,
. ,
0,
,
. , 0,
,
-
. , Jn
, .
Jn h, . (30)
li Qli . h, ,
Jm, . , (cosm
cosn) , .
, Jn
. ,
.
4.13 -
, ,
- ,
Heisenberg Bohr .
Heisenberg,
,
. ,
Heisenberg
.
Compton Heisenberg
Compton
(., ,
,
,
). ,
.
-
Heisenberg , ,
.
,
.
, Heisenberg
,
. ,
. ,
,
, ,
.
Brown
.
10 12, ,
-
. , -
, , ..,
. ,
( , ,
, .).
- . ,
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,
.
-
Heisenberg.
, , ,
-
. , -
-
, ,
, ,
.
,
,
h,
Heisenberg ,
- - .
;
, . (25),
. li Qli , , , pli
qli . -
. . ,
(.., ) li Qli
pli qli - .
, - (
, )
.
, .
-
, li Qli , . ,
. , Jn = nh . (24)
h ( ). -
= nh . ,
. -
-
. ,
En nhv. ,
E= nh +
(
).
,
. , , -
.
, Bohr
Heisenberg,
.
Bohr
- (
). -
, ,
.
, Einstein, Rosen Podolsky.
4,
, - .
,
.
, ,
. , ,
-
,
;
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,
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, 4,
spin , . ,
,
spin
.
,
. .
.
,
,
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-
.
,
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,
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, -
. , -
, .
, .
-
4.14 ,
-
.
,
,
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). ,
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.)
, .
Dirac
, .
. ,
(, , .) .
.
, ,
,
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,
.
,
.
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). ,
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.
,
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1. ( )
: .
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.
.
.
, .
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